If, there are large gaps along the perimeter. I would replace the baseboards with thicker boards. The 3 1/4" bases are only 1/2-5/8" thick A 3/4" thick baseboard will cover up gaps. A shoe or quarter will look horrible up against a short base.

Are the 3/4" baseboard significantly more expensive than shoe mold or quarter rounds? One of the bids estimated 190 feet of plastic(?) shoe mold @ $2.75 for a total of $522. I'm suffering sticker shock but maybe it's labor-intensive.

Lumber is expensive in general. Yes, a 3/4" baseboard system will cost more. It's a two piece base board system. You will need 3/4" flat stock for the base and a base cap, which is the top profile. You can fully customize the look, since the cap is available in a variety of profiles.

We had to do the same in removing broadloom in our 50’s house. We installed quarter round which had to be thick enough to cover gaps where the small baseboards met the floor. Not my favourite choice as it is a bit dated looking. Didn’t want to replace baseboards, as removing old would have damaged the walls and didn’t want to plaster and paint all walls. Toe kicks are concave I think, so I thought would have collected more dust. Looking back I might have investigated something more square looking rather than quarter rounds, but again, some of the gaps were pretty big and needed more coverage.

Update: I went with quarter rounds and they look fine. Or, to be more specific, I don't notice them which is the way I like it.